PolandBall and Gifts
Description
It's Christmas time! PolandBall and his friends will be giving themselves gifts. There are n Balls overall. Each Ball has someone for whom he should bring a present according to some permutation p, pi ≠ i for all i.
Unfortunately, Balls are quite clumsy. We know earlier that exactly k of them will forget to bring their gift. A Ball number i will get his present if the following two constraints will hold:
- Ball number i will bring the present he should give.
- Ball x such that px = i will bring his present.
What is minimum and maximum possible number of kids who will not get their present if exactly k Balls will forget theirs?
The first line of input contains two integers n and k (2 ≤ n ≤ 106, 0 ≤ k ≤ n), representing the number of Balls and the number of Balls who will forget to bring their presents.
The second line contains the permutation p of integers from 1 to n, where pi is the index of Ball who should get a gift from the i-th Ball. For all i, pi ≠ i holds.
You should output two values — minimum and maximum possible number of Balls who will not get their presents, in that order.
Input
The first line of input contains two integers n and k (2 ≤ n ≤ 106, 0 ≤ k ≤ n), representing the number of Balls and the number of Balls who will forget to bring their presents.
The second line contains the permutation p of integers from 1 to n, where pi is the index of Ball who should get a gift from the i-th Ball. For all i, pi ≠ i holds.
Output
You should output two values — minimum and maximum possible number of Balls who will not get their presents, in that order.
Samples
5 2
3 4 1 5 2
2 4
10 1
2 3 4 5 6 7 8 9 10 1
2 2
Note
In the first sample, if the third and the first balls will forget to bring their presents, they will be th only balls not getting a present. Thus the minimum answer is 2. However, if the first ans the second balls will forget to bring their presents, then only the fifth ball will get a present. So, the maximum answer is 4.